feat: add blas/base/sgemm

[aman-095]

Progresses #2039.

Description

What is the purpose of this pull request?

This RFC proposes to add a routine to perform one of the matrix-matrix operation C = α*op(A)*op(B) + β*C where op(A) is one of the op(A) = A, or op(A) = A^T, α and β are scalars, A, B, and C are matrices, with op(A) an M by K matrix, op(B) a K by N matrix and C an M by N matrix as defined in BLAS Level 3 routines. Specifically adding @stdlib/blas/base/sgemm is proposed.

Related Issues

Does this pull request have any related issues?

This pull request:

• progresses [RFC]: Add BLAS bindings and implementations for linear algebra (tracking issue) #2039.

Questions

Any questions for reviewers of this pull request?

No.

Other

Any other information relevant to this pull request? This may include screenshots, references, and/or implementation notes.

No.

Checklist

Please ensure the following tasks are completed before submitting this pull request.

• Read, understood, and followed the contributing guidelines.

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@stdlib-js/reviewers

[kgryte]

/stdlib update-copyright-years

[kgryte]

@aman-095 To reduce the risk of benchmark workflow timeout, let's reduce the max power in the benchmark files to 5, rather than 6.

[aman-095]

@kgryte I tried reducing the max power to 5, but it still takes a lot of time. Can we reduce it further?

[kgryte]

@aman-095 Yeah, reducing to 4 should be fine. We can increase again for dgemm. From testing locally, the repeated calls to f32() slow things down a bit. Usually doesn't matter too much, but for gemm it does due to the sheer number of repeated calls.

[kgryte]

@aman-095 Looking at the test fixtures, it is not clear why the strides are changing when parameterizing whether a transpose should be performed. E.g., for ca_cb_cc_nta_tb.json, B is a 3x4 column-major matrix. In which case, the strides should be [1,4], as they are in the fixture.

{
  "transA": "no-transpose",
  "transB": "transpose",
  "M": 2,
  "N": 4,
  "K": 3,
  "alpha": 1.0,
  "A": [ 1.0, 4.0, 2.0, 5.0, 3.0, 6.0 ],
  "strideA1": 1,
  "strideA2": 2,
  "offsetA": 0,
  "B": [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ],
  "strideB1": 1,
  "strideB2": 4,
  "offsetB": 0,
  "beta": 1.0,
  "C": [ 1.0, 5.0, 2.0, 6.0, 3.0, 7.0, 4.0, 8.0 ],
  "strideC1": 1,
  "strideC2": 2,
  "offsetC": 0,
  "C_out": [ 7.0, 20.0, 8.0, 21.0, 9.0, 22.0, 10.0, 23.0 ]
}

However, for the no-transpose fixture ca_cb_cc_nta_ntb.json, you have

{
  "transA": "no-transpose",
  "transB": "no-transpose",
  "M": 2,
  "N": 4,
  "K": 3,
  "alpha": 1.0,
  "A": [ 1.0, 4.0, 2.0, 5.0, 3.0, 6.0 ],
  "strideA1": 1,
  "strideA2": 2,
  "offsetA": 0,
  "B": [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ],
  "strideB1": 1,
  "strideB2": 3,
  "offsetB": 0,
  "beta": 1.0,
  "C": [ 1.0, 5.0, 2.0, 6.0, 3.0, 7.0, 4.0, 8.0 ],
  "strideC1": 1,
  "strideC2": 2,
  "offsetC": 0, 
  "C_out": [ 7.0, 20.0, 8.0, 21.0, 9.0, 22.0, 10.0, 23.0 ]
}

with the strides for B being [1,3]. This doesn't appear correct. The strides should be for B, not op(B), as the transA and transB state what should happen inside the implementation, not how B is provided.

I believe this needs to be addressed across the various test fixtures. For the benchmarks, we handle this correctly.

[aman-095]

@kgryte We use matrices of dimension N*N for benchmarks, so we don't need to bother about this. But, in the standard lapack implementation they say that M, N, and K are dimensions based on op(X).

[aman-095]

In the test suites I have used matrices:

A =    [1, 2, 3]
       [4, 5, 6]
       
B =    [1, 1, 1, 1]
       [1, 1, 1, 1]
       [1, 1, 1, 1]

C =    [1, 2, 3, 4]
       [5, 6, 7, 8]

Now, based on the operation say if we have transB = transpose the operation would be α*A*B^T + β*C where A = (2X3) but here B^T should have the dimension of (3X4), and hence the B which I pass as input changes to B^T (4X3) and then based on 'row-major' or 'column-major' we have strides.

[kgryte]

@aman-095 You're right. Thanks for correcting me.

[kgryte]

LGTM. Thanks, @aman-095!

[Pranavchiku]

+9000 lines of code, with review! 🙇‍♂️🚀